The Collaborative International Dictionary
Bower \Bow"er\ (bou"[~e]r), n. [G. bauer a peasant. So called from the figure sometimes used for the knave in cards. See Boor.] One of the two highest cards in the pack commonly used in the game of euchre.
Right bower, the knave of the trump suit, the highest card (except the ``Joker'') in the game.
Left bower, the knave of the other suit of the same color as the trump, being the next to the right bower in value.
Best bower or Joker, in some forms of euchre and some other games, an extra card sometimes added to the pack, which takes precedence of all others as the highest card.
Wiktionary
n. (context euchre English) The jack of the trump suit, the highest card in the game except the joker.
Usage examples of "right bower".
But he did go along, and he was dropped and left in front of the bank because he was your right bower, and his being killed there would pin the trick to you.
So you see there was simply nothing to be done now, but play their right bower—.